NASA Dataset Final Project
David Han
6/28/2019
Linear Regressions
I created several linear regression models using temperature as the dependent variable.
Temperature vs. Low Cloud Coverage
temp_lowc <- lm(temperature ~ cloudlow,data = combine)
temp_lowc %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 277.7132586 2.7138125 102.33325 5.691620e-78
## 2 cloudlow 0.6569496 0.1328456 4.94521 5.022951e-06lowcg <- ggplot(combine,aes(x=cloudlow,y=temperature))+geom_point()+
xlab("Low Cloud Coverage")+ylab("Temperature")+
geom_abline(intercept=277.7133,slope=0.6569,col="red")
lowcg
Temperature vs. Middle Cloud Coverage
temp_midc <- lm(temperature ~ cloudmid,data = combine)
temp_midc %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 313.376097 2.2739709 137.81008 5.642312e-87
## 2 cloudmid -1.167782 0.1110144 -10.51919 4.670486e-16midcg <- ggplot(combine,aes(x=cloudmid,y=temperature))+geom_point()+
xlab("Middle Cloud Coverage")+ylab("Temperature")+
geom_abline(intercept=313.376,slope=-1.168,col="red")
midcg
Temperature vs. High Cloud Coverage
temp_highc <- lm(temperature ~ cloudhigh,data = combine)
temp_highc %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 298.8933145 1.7554467 170.266243 2.193430e-93
## 2 cloudhigh -0.8519088 0.1541152 -5.527739 5.221285e-07highcg <- ggplot(combine,aes(x=cloudhigh,y=temperature))+geom_point()+
xlab("High Cloud Coverage")+ylab("Temperature")+
geom_abline(intercept=298.8933,slope=-0.8519,col="red")
highcg
Temperature vs. Ozone
temp_ozone <- lm(temperature ~ ozone,data = combine)
temp_ozone %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 337.8292030 12.16953566 27.760238 1.634629e-39
## 2 ozone -0.1525832 0.03904494 -3.907888 2.124625e-04ozoneg <- ggplot(combine,aes(x=ozone,y=temperature))+geom_point()+
xlab("Ozone Level")+ylab("Temperature")+
geom_abline(intercept=337.8292,slope=-0.1526,col="red")
ozoneg
Temperature vs. Surface Temperature
temp_surftemp <- lm(temperature ~ surftemp,data = combine)
temp_surftemp %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 86.0301279 10.9520922 7.855132 3.376424e-11
## 2 surftemp 0.7002365 0.0374963 18.674818 6.705231e-29surfg <- ggplot(combine,aes(x=surftemp,y=temperature))+geom_point()+
xlab("Surface Temperature")+ylab("Temperature")+
geom_abline(intercept=86.0301,slope=0.7002,col="red")
surfg
Temperature vs. Pressure
temp_pres <- lm(temperature ~ pressure,data = combine)
temp_pres %>% tidy() %>% as.data.frame()## term estimate std.error statistic p.value
## 1 (Intercept) 259.84483680 20.06505232 12.950120 2.938691e-20
## 2 pressure 0.03408459 0.02234757 1.525203 1.317141e-01presg <- ggplot(combine,aes(x=pressure,y=temperature))+geom_point()+
xlab("Atmospheric Pressure")+ylab("Temperature")+
geom_abline(intercept=259.84484,slope=0.03408,col="red")
presg
Used to combine all graphs into one figure.
figure <- ggarrange(lowcg,midcg,highcg,ozoneg,surfg,presg ,ncol = 3,nrow=2)
figure
Regression with Multiple Variables
From the linear regressions, pressure was the only variable that did not correlate with temperature. Therefore, the multiple linear regression model will not use that variable for predictions.
model <- lm(temperature ~ cloudlow+cloudmid+cloudhigh+ozone+surftemp,data=combine)
summary(model)##
## Call:
## lm(formula = temperature ~ cloudlow + cloudmid + cloudhigh +
## ozone + surftemp, data = combine)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.7001 -1.7232 -0.0064 1.7982 4.8737
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 20.43522 22.89516 0.893 0.375
## cloudlow -0.65061 0.10505 -6.194 4.27e-08 ***
## cloudmid 0.16998 0.10875 1.563 0.123
## cloudhigh -0.43951 0.08269 -5.315 1.35e-06 ***
## ozone 0.01669 0.02003 0.833 0.408
## surftemp 0.95383 0.06855 13.915 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.427 on 66 degrees of freedom
## Multiple R-squared: 0.9261, Adjusted R-squared: 0.9205
## F-statistic: 165.3 on 5 and 66 DF, p-value: < 2.2e-16Predictions
Chose 50 random data points from the NASA data set (some listed below):
temp_pred <- sample_n(dfnasa,50)
head(temp_pred)## lat long month year cloudhigh cloudlow cloudmid ozone
## 1 16.234783 -98.77391 7 1997 27.5 13.0 22.5 278
## 2 23.721739 -93.76522 11 1996 2.0 34.0 6.5 262
## 3 18.730435 -103.78261 5 1998 1.0 14.5 3.5 278
## 4 33.704348 -108.79130 1 1998 6.5 8.5 21.0 316
## 5 8.747826 -73.73043 9 2000 45.5 7.0 22.0 262
## 6 23.721739 -63.71304 11 1998 4.5 30.5 6.5 268
## pressure surftemp temperature
## 1 945 298.3 301.0
## 2 1000 298.7 297.8
## 3 980 301.0 303.6
## 4 835 277.3 280.5
## 5 990 294.6 303.2
## 6 1000 299.2 299.2Data frame of 50 random rows from the NASA data set.
model_usage <- temp_pred %>% select(cloudhigh,cloudlow,cloudmid,ozone,surftemp)
real_temp <- temp_pred %>% select(temperature)
head(model_usage)## cloudhigh cloudlow cloudmid ozone surftemp
## 1 27.5 13.0 22.5 278 298.3
## 2 2.0 34.0 6.5 262 298.7
## 3 1.0 14.5 3.5 278 301.0
## 4 6.5 8.5 21.0 316 277.3
## 5 45.5 7.0 22.0 262 294.6
## 6 4.5 30.5 6.5 268 299.2The model_usage variable was used to find the prediction while storing the actual temperature in real_temp.
model_predictions <- model_usage %>% add_predictions(model)
head(model_predictions)## cloudhigh cloudlow cloudmid ozone surftemp pred
## 1 27.5 13.0 22.5 278 298.3 292.8818
## 2 2.0 34.0 6.5 262 298.7 287.8213
## 3 1.0 14.5 3.5 278 301.0 302.8984
## 4 6.5 8.5 21.0 316 277.3 285.3877
## 5 45.5 7.0 22.0 262 294.6 284.9932
## 6 4.5 30.5 6.5 268 299.2 289.5767Graph of Predictions
actual_preddf <- data.frame(cbind(real_temp, model_predictions$pred))
colnames(actual_preddf) = c("real","prediction")
ggplotly(ggplot(actual_preddf)+geom_point(aes(x=real,y=prediction))+
geom_abline(intercept=0,slope=1,col="darkturquoise",size=1)+
xlab("Real Temperature")+ylab("Predicted Temperature"))